electronics

In an RL series AC circuit, R=100 ohms, L=50 mH. The supply voltage through the resistor obeys the equation v(t)=311 sin314t volts.Calculate:
(a)the frequency of the AC voltage.
ω = 314
f = ω / 2π = 314 / 2π
= 50Hz
(b)the rms voltage of the supply voltage.
Vrms = Vo / √2 = 311 / √2
= 220v
(c)the reactance of the circuit.
XL = ωL = 314x50x10-3
= 15.7Ω
(d)the impedance of the circuit.
Z = √(1002 + 15.72)
= 101.2Ω
(e)the circuit current.
Irms = Vrms / X = 220 / 101.2
= 2.17A
(f)the peak current.
Io = Irms√2 = 2.17√2
= 3.07A
(g)the rms power delivered to the circuit.
P = Irms2 R = 2.172 x 100
= 471W